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A130757
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Triangular table of coefficients of Laguerre-Sonin polynomials n!*2^(n-m)*L(n,1/2,x).
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6
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1, 3, -1, 15, -10, 1, 105, -105, 21, -1, 945, -1260, 378, -36, 1, 10395, -17325, 6930, -990, 55, -1, 135135, -270270, 135135, -25740, 2145, -78, 1, 2027025, -4729725, 2837835, -675675, 75075, -4095, 105, -1, 34459425, -91891800, 64324260, -18378360, 2552550, -185640, 7140, -136
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| These polynomials appear in the radial l=0 (s) wave functions of the isotropic three dimensional harmonic quantum oscillator with the dimensionless variable x=(r/L)^2 with r>=0 and L^2=h/(m*f0). h is Planck's constant and m and f0 are the mass and the frequency of the oscillator.
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LINKS
| M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 775, 22.3.9.
W. Lang, First ten rows and more.
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FORMULA
| a(n,m)= n!*(2^(n-m))*L(1/2,n,m) with L(1/2,n,m)=((-1)^m)*binomial(n+1/2,n-m)/m!, n>=m>=0, else 0.
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EXAMPLE
| [1]; [3,-1]; [15,-10,1]; [105,-105,21,-1]; [945,-1260,378,-36,1]; ...
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CROSSREFS
| Cf. A021009 (Coefficient table of n!*L(n, 0, x).
Row sums (signed) give A131441. Row sums (unsigned) give A066224.
Sequence in context: A147453 A147020 A134685 * A014621 A144006 A193966
Adjacent sequences: A130754 A130755 A130756 * A130758 A130759 A130760
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KEYWORD
| sign,tabl,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de) Jul 13 2007
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